##### Preview Activity2.5.1

We will begin by considering a more familiar situation; namely, the function $$f(x) = x^2\text{,}$$ which takes a real number $$x$$ as an input and produces its square $$x^2$$ as its output.

1. What is the value of $$f(3)\text{?}$$

2. Can we solve the equation $$f(x) = 4\text{?}$$ If so, is the solution unique?

3. Can we solve the equation $$f(x) = -10\text{?}$$ If so, is the solution unique?

4. Sketch a graph of the function $$f(x)=x^2$$ in Figure 1

5. Remember that the range of a function is the set of all possible outputs. What is the range of the function $$f\text{?}$$

6. We will now consider functions having the form $$g(x)=mx\text{.}$$ Draw a graph of the function $$g(x) = 2x$$ on the left in Figure 2.

7. Draw a graph of the funcion $$h(x) = -\frac13 x$$ on the right of Figure 2.

8. Remember that composing two functions means we use the output from one function as the input into the other. That is, $$g\circ h(x) = g(h(x))\text{.}$$ What function results from composing $$g\circ h(x)\text{?}$$ How is the composite function related to the two functions $$g$$ and $$h\text{?}$$

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