Question

The rule of a function f is given. Write an algebraic formula for f(x).

a. Square the input, subtract 16, and take the square root of the result.

b. Cube the input, multiply by 3, add 5, and divide the result by the input. 

Answer 1

Let the input be $(x)$

Then step 1: square the input = $x^2$

Step 2: subtract 16 $=x^2-16$

Step 3: take the square root of the result = $\sqrt{x^2-16}$

So $f(x)=\sqrt{x^2-16}$

b

Let the input be $(x)$

Then step 1: cube the input = $x^3$

Step 2: multiply by 3 $=3x^3$

Step 3: add 5 result = $3x^3+5$

Step 4: divide result by input

So $f(x)=\frac{3x^3+5}{x}$