Precalculus Combining and Composing Functions Quiz: 10 Questions with Explanations

A 14B 11C 10D 9

g(4) = 8, then f(8) = 11. Computing g(f(4)) = 14 reverses the order.

A 8B 4C 9D 10

f(3) = 9, then g(9) = 8. The answer 4 comes from f(g(3)).

A \((2x+1)^{2}\)B \(2x^{3}+x^{2}\)C \(2x^{2}+x\)D \(2x^{2}+1\)

Substitute x^2 for x in f: 2(x^2) + 1. Squaring (2x+1) is g(f(x)).

A 0B 2C 5D 3

g(1) = 0 and f(0) = 2. The value 5 is f(1).

A \(x\neq 6\)B \(x\neq -6\)C \(x\ge 6\)D All real numbers

The denominator g(x) cannot be 0, so x cannot be 6.

A \(f=4x+1,\ g=\sqrt{x}\)B \(f=x+1,\ g=\sqrt{4x}\)C \(f=\sqrt{x},\ g=4x+1\)D \(f=\sqrt{x}+1,\ g=4x\)

The inside expression 4x + 1 is g and the square root is the outer function f.

A \((4,\infty)\)B \([4,\infty)\)C \([0,\infty)\)D \((-\infty,4]\)

The radicand x – 4 must be at least 0, so x >= 4, with 4 included.

A \(f(g(x))=g(f(x))\)B \(f(g(x))=3x+15\)C \(f(g(x))\neq g(f(x))\)D \(g(f(x))=3x+5\)

f(g(x)) = 3x + 5 but g(f(x)) = 3x + 15, so the order matters.

A \(\$40.50\)B \(\$45\)C \(\$35\)D \(\$40\)

d(50) = 45, then c(45) = 40. Reversing the order gives 0.9(45) = 40.50.

A Apply g first, then fB Apply f first, then gC Multiply f(x) by g(x)D Add f(x) and g(x)

In f(g(x)) the inner function g acts on x first.