Question

Let the functions f,g, and h be defined by the equations on the right. Evaluate the indicated function without finding an equation for the function.

g(f[h(2)])
f(x)=4x−3
g(x)=2x−1
h(x)=x2+3x+1
g(f[h(2)])=

Answer 1

Explanation:

To evaluate the function g(f[h(2)]), we need to substitute the value of 2 into the function h(x), then take the result and substitute it into the function f(x), and finally substitute the result into the function g(x).

Given:

f(x) = 4x - 3

g(x) = 2x - 1

h(x) = x^2 + 3x + 1

First, evaluate h(2):

h(2) = (2)^2 + 3(2) + 1

= 4 + 6 + 1

= 11

Next, substitute h(2) into f(x):

f(h(2)) = f(11) = 4(11) - 3 = 44 - 3 = 41

Finally, substitute f(h(2)) into g(x):

g(f[h(2)]) = g(41) = 2(41) - 1 = 82 - 1 = 81

Therefore, g(f[h(2)]) evaluates to 81.