Math GRE subject test question

In summary: So the graph of y= e^x+ x- 2 will cross the x-axis only once. And that is when x= 1. In summary, the equation e^x + x - 2 = 0 has only one real solution in the interval [0,1], and there are no real solutions outside of this interval. Therefore, the correct answer is B) k = 1 and n = 0.
  • #1
PsychonautQQ
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10
Let k be the number of real solutions to the equation e^x + x - 2 = 0 in the interval [0,1] and let n be the number of real solutions NOT on the interval [0,1]. Which of the following are true?

A) k = 0 and n = 1
B) k = 1 and n = 0
C) k = n = 1
D) k > 1
E) n > 1

Can anyone help me understand this? I'm thinking that the answer is B, because if x = 1 then the equation will be greater than zero, and the equation starts below the x-axis. So somewhere in the interval [0,1], the line must cross the x=axis. Hence B is the answer. Is this correct?
 
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  • #2
PsychonautQQ said:
Let k be the number of real solutions to the equation e^x + x - 2 = 0 in the interval [0,1] and let n be the number of real solutions NOT on the interval [0,1]. Which of the following are true?

A) k = 0 and n = 1
B) k = 1 and n = 0
C) k = n = 1
D) k > 1
E) n > 1

Can anyone help me understand this? I'm thinking that the answer is B, because if x = 1 then the equation will be greater than zero, and the equation starts below the x-axis. So somewhere in the interval [0,1], the line must cross the x=axis. Hence B is the answer. Is this correct?
Maybe or maybe not. The real question is whether the graph of the function f(x) = ex + x - 2 crosses the x-axis outside the interval [0, 1]. If it does so once, then C would be the answer.

How do you know for certain that there is only one x-intercept? Hint: take the derivative of f.

Minor quibble: an equation is not greater than zero, less than zero, or equal to zero. An equation is a statement that two quantities or expressions are equal. An inequality is a statement that one expression is larger than, or smaller than, another.
 
  • #3
I think it is simpler to convert [itex]e^x+ x- 2= 0[/itex] to [itex]e^x= 2- x[/itex].

Now, even a rough graph of [itex]y= e^x[/itex] and [itex]y= 2- x[/itex] will give the answer.
 

FAQ: Math GRE subject test question

What is the Math GRE subject test?

The Math GRE subject test is an exam designed to assess a student's knowledge and understanding of advanced mathematical concepts typically covered in undergraduate math courses. It is often required for admission to graduate programs in math, physics, and related fields.

What topics are covered on the Math GRE subject test?

The Math GRE subject test covers a wide range of topics, including calculus, linear algebra, abstract algebra, real analysis, and discrete mathematics. It also includes questions on geometry, probability, and statistics.

How is the Math GRE subject test scored?

The Math GRE subject test is scored on a scale of 200-990, with 200 being the lowest possible score and 990 being the highest. The score is based on the number of correct answers, with no penalty for incorrect answers. The average score is around 600.

How should I prepare for the Math GRE subject test?

It is recommended to start preparing for the Math GRE subject test several months in advance. This can include reviewing textbooks, taking practice tests, and seeking help from a tutor or study group. It is also important to familiarize yourself with the test format and timing.

How often is the Math GRE subject test offered?

The Math GRE subject test is offered three times a year, in September, October, and April. It is important to check the test dates and register early, as seats may fill up quickly. The test can be taken multiple times, but only once per testing cycle.

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