Question

Find f(g(1)) and g(f(1))
F(x)=x^2+2;g(x)=2x-5

Answer 1

Explanation:

Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.

First, let’s find f(g(1)). We start by evaluating the inner function g(1):

g(1) = 2 * 1 - 5 = -3

Now we can use this result as the input for the outer function f(-3):

f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11

Next, let’s find g(f(1)). We start by evaluating the inner function f(1):

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

Now we can use this result as the input for the outer function g(3):

g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1

So, f(g(1)) = 11 and g(f(1)) = 1.