when is (f of h)(5) if f(x)=2x^2-5 and h(x)= sqrt x-3 then simplify answer to equal to -1
To find (f of h)(5), we first substitute x = 5 in function h(x):
h(5) = sqrt(5) - 3 = sqrt(5) - 3.
Next, we substitute h(5) into function f(x):
f(h(5)) = 2(h(5))^2 - 5
= 2(sqrt(5) - 3)^2 - 5
= 2(5 - 6(sqrt(5)) + 9) - 5
= 10 - 12(sqrt(5)) + 18 - 5
= 23 - 12(sqrt(5)).
Therefore, (f of h)(5) = 23 - 12(sqrt(5)). To simplify the answer to equal -1, we need to set 23 - 12(sqrt(5)) = -1:
23 - 12(sqrt(5)) = -1
12(sqrt(5)) = 24
sqrt(5) = 24/12
sqrt(5) = 2.
As 2 is not the square root of 5, the initial statement that (f of h)(5) equals -1 does not hold true based on the calculated value of 23 - 12(sqrt(5)).