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### Section 1-1 : Review : Functions

33. Compute $$\left( {f \circ g} \right)\left( x \right)$$ and $$\left( {g \circ f} \right)\left( x \right)$$ for $$f\left( x \right) = 4x - 1$$, $$g\left( x \right) = \sqrt {6 + 7x}$$.

Show Solution

Not much to do here other than to compute each of these.

\begin{align*}\left( {f \circ g} \right)\left( x \right) & = f\left[ {g\left( x \right)} \right] = f\left[ {\sqrt {6 + 7x} } \right] = 4\sqrt {6 + 7x} - 1\\ & \\ \left( {g \circ f} \right)\left( x \right) & = g\left[ {f\left( x \right)} \right] = g\left[ {4x - 1} \right] = \sqrt {6 + 7\left( {4x - 1} \right)} = \sqrt {28x - 1} \end{align*}