Solving f(x) = 5^sqrt(2(x^2)-1)

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The function f(x) = 5^sqrt(2(x^2)-1) has a range of (1, infinity), confirming that the output values (y-values) start from 1 and extend to infinity. When x = -2, f(-2) equals 5^sqrt(7), and f(sqrt(2)/2) equals 1. The discussion clarifies that "range" typically refers to y-values, while "domain" is used for x-values. There is some confusion regarding terminology, as some participants have seen "range" applied to x-values in different contexts. Overall, the focus remains on understanding the correct definitions of range and domain in relation to the function.
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f(x)=5^sqrt(2(x^2)-1)

I got that range is (1, to infinity)

Is it correct?
 
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What does f equal if x = -2 ?
 
5^sqrt(7). If x=sqrt(2)/2, then I get F(x)=1
 
Isn't x= sqrt(1/2) the lowest you can go?
 
By range, do you mean the range of x-values or y-values ?

If it's for the y-values then your range of 1 - infinity is correct.

If it's for the x-values, then that's a bit different.
 
For y values. They teach us to call x-values domain.
 
That's right.
I use domain for x-values and co-domain for y-values.
But I've seen range used for x-values before.
 
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