Question

If \(f\left( x \right) = x + {\bf{4}}\) and \(h\left( x \right) = {\bf{4}}x - {\bf{1}}\), find a function g such that \(g \circ f = h\).

Short answer

The function is \(g\left( x \right) = 4x - 17\).

Step-by-step solution

Write the composite function \(g \circ f\)

Thecomposite function\(g \circ f\) can be expressed as:

\(\begin{aligned}g \circ f\left( x \right) &= g\left( {f\left( x \right)} \right)\\ &= g\left( {x + 4} \right)\\ &= 4x - 1\\ &= h\left( x \right)\\ &= 4\left( {x + 4} \right) - 17\end{aligned}\)

Find the function \(g\left( x \right)\) by using \(g \circ f\)

The function \(g\left( x \right)\) can be expressed as:

\(g\left( x \right) = 4x - 17\)

The function is \(g\left( x \right) = 4x - 17\).