If f(x) = 2x − 1 and g(x) = x^2 + 5, find (f of g)(−3) and (g of f)(2).
Can anyone help ?
Yes, I can help you with that. To find (f of g)(−3), we need to first evaluate g(x) at x = -3, and then substitute the result into f(x). Here's how you do it step by step:
Step 1: Evaluate g(x) at x = -3.
g(x) = x^2 + 5
g(-3) = (-3)^2 + 5
= 9 + 5
= 14
Step 2: Substitute the result from Step 1 into f(x).
f(x) = 2x - 1
f(g(-3)) = f(14)
= 2(14) - 1
= 28 - 1
= 27
Therefore, (f of g)(-3) = 27.
Let's now find (g of f)(2). Similarly, we need to evaluate f(x) at x = 2, and substitute the result into g(x).
Step 1: Evaluate f(x) at x = 2.
f(x) = 2x - 1
f(2) = 2(2) - 1
= 4 - 1
= 3
Step 2: Substitute the result from Step 1 into g(x).
g(x) = x^2 + 5
g(f(2)) = g(3)
= 3^2 + 5
= 9 + 5
= 14
Therefore, (g of f)(2) = 14.
Hence, (f of g)(−3) = 27 and (g of f)(2) = 14.