Precalculus · Problem 83

Relations and Functions — Stitz & Zeager

Mathematics — Precalculus · function-arithmetic

Problem

Using the graphs of y=f(x)y = f(x) and y=g(x)y = g(x) given in the text, find (fg)(1)(fg)(1).
Intuitive explanation

The product of two functions (fg)(x)(fg)(x) means you multiply their output values together at the same input. So to find (fg)(1)(fg)(1), you need to read the yy-value of each graph at x=1x = 1, then multiply those two values. It's a straightforward application of function composition notation—just remember you're multiplying the outputs, not composing them.

Intuitive explanation

The product of two functions (fg)(x)(fg)(x) means you multiply their output values together at the same input. So to find (fg)(1)(fg)(1), you need to read the yy-value of each graph at x=1x = 1, then multiply those two values. It's a straightforward application of function composition notation—just remember you're multiplying the outputs, not composing them.

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