Question

Given f(x) = 2x + 3 and u = x², find f(u) in terms of x.

Answer 1

Function composition is used to find f(u) given f(x) = 2x + 3 and u = x², resulting in f(u) = 2x² + 3 in terms of x.

Step-by-step explanation:

To find f(u) in terms of x, given f(x) = 2x + 3 and u = x², we substitute u into the function f. This process is called function composition. The step-by-step process is as follows:

• Write the original function: f(x) = 2x + 3.
• Substitute u for x in the given function: f(u) = 2u + 3.
• Since we know that u = x², we can substitute x² for u: f(u) = f(x²) = 2x² + 3.

Therefore, in terms of x, f(u) is 2x² + 3.