when is (f of h)(5) if f(x)=2x^2-5 and h(x)= sqrt x-3
how does it equal to -1?
First, we need to find (f of h)(x). This means we need to plug h(x) into f(x).
Given f(x) = 2x^2 - 5 and h(x) = sqrt(x) - 3, substituting h(x) into f(x) gives us:
(f of h)(x) = f(h(x))
= 2(sqrt(x) - 3)^2 - 5
= 2(x - 6(sqrt(x)) + 9 - 5
= 2x - 12(sqrt(x)) + 4
Now, to find (f of h)(5), we substitute x = 5 into our expression:
(f of h)(5) = 2(5) - 12(sqrt(5)) + 4
= 10 - 12(some value) + 4
= 10 - 12(2.236) + 4
≈ 10 - 26.832 + 4
≈ -12.832 + 4
= -8.832
Therefore, (f of h)(5) is approximately equal to -8.832, not -1.