Range of a function, very simple & basic question

[sachin_naik04]

Just go through the following problem

Question 1:find the range of the following function
f(x)=3x²+4 for -4≤x≤3

Answer:
rewriting -4≤x≤3
step1. 0≤x²≤16
step2. multiply 3 for the entire step 1.
step4. add 4 for the entire step1.
step5. 4≤f(x)≤52

so the above problem i have understood

now how do i solve the following problem using the same method as above, because the following problem is a bit different from the first one, and i get a reverse answer

Question 2: find the range of the following function
f(x)=9-2x² for -3≤x≤3

rewriting -3≤x≤3
step 1. 0≤x²≤9 now is this step correct?, i don't think so.
step 2. ?
step 3. ?
step 4. ?

please note: i cannot find the range directly because each step carries marks

 

[willem2]

The step is correct. .

if you square x<=3 that will give you (x^2 <=9) or (x<0)
if you square x>=-3 that will give you ((x^2 <= 9) or (x>0))

if both are true you just get (x^2 <= 9)

 

[HallsofIvy]

Just go through the following problem

Question 1:find the range of the following function
f(x)=3x²+4 for -4≤x≤3

Answer:
rewriting -4≤x≤3
step1. 0≤x²≤16
step2. multiply 3 for the entire step 1.
step4. add 4 for the entire step1.
step5. 4≤f(x)≤52

so the above problem i have understood

now how do i solve the following problem using the same method as above, because the following problem is a bit different from the first one, and i get a reverse answer

Question 2: find the range of the following function
f(x)=9-2x² for -3≤x≤3

rewriting -3≤x≤3
step 1. 0≤x²≤9 now is this step correct?, i don't think so.

Yes, it is correct. Why would you not think so?

step 2. ?

Multiplying each part of the inequality by negative 2 reverses the inequality:
$-18\le x^2\le 0$
Since you say you got a "reverse answer" that may have been your mistake.

step 3. ?

Add 9 to each part.

step 4. ?

Write down your answer!

please note: i cannot find the range directly because each step carries marks

 

[sachin_naik04]

@HallsofIvy

oh thanks a lot, that helped me