# Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 259: 92

The value of $\left( f\circ g \right)\left( 1 \right)$ is $3$.

#### Work Step by Step

Consider the above graph: The curve ${{C}_{1}}$, shows the values of the function $f\left( x \right)$ and curve ${{C}_{2}}$ shows the values of the function $g\left( x \right)$. The composition of f with g can be defined as the function $\left( f\circ g \right)$ and $\left( f\circ g \right)\left( x \right)$ which is equivalent to $f\left( g\left( x \right) \right)$. Consider the equation below: $\left( f\circ g \right)\left( 1 \right)=f\left( g\left( 1 \right) \right)$ Here, $g\left( 1 \right)=-5$. Then, $f\left( g\left( 1 \right) \right)=f\left( -5 \right)$ And the value of $f\left( -5 \right)=3$. Hence, $\left( f\circ g \right)\left( 1 \right)=3$ Hence, the value of $\left( f\circ g \right)\left( 1 \right)$ is $3$.

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