To find the composition of functions g(f(x)) and evaluate it at a specific value, we need to substitute f(x) into g(x) and simplify the expression.
Given:
f(x) = 2x - 1
g(x) = x^2 + 2
To find g(f(x)), substitute f(x) into g(x):
g(f(x)) = (2x - 1)^2 + 2
Expanding the expression:
g(f(x)) = (2x - 1)(2x - 1) + 2
= 4x^2 - 4x - 4x + 1 + 2
= 4x^2 - 8x + 3
Now, to find g(f(3)), substitute x = 3 into g(f(x)):
g(f(3)) = 4(3)^2 - 8(3) + 3
= 4(9) - 24 + 3
= 36 - 24 + 3
= 15
Therefore, g(f(3)) = 15. Happy to help