By Christopher Thomas

Updated on Oct 1, 2011

To review these concepts, go to Calculus Functions Study Guide.

**Calculus Functions Practice Questions**

- Find the value of
*f*(5) when*f*(*x*) = 2*x*– 1. - Find the value of
*g*( – 3) when*g*(*x*) =*x*^{3}+*x*^{2}+*x*+ 1. - Find the value of
*h*when*h*(*t*) =*t*^{2}+ - Find the value of
*f*(7) when*f*(*x*) = 2. - Find the value of
*k*( 4) when*k*(*u*) =*u*^{2}+2*u*– . - Find the value of
*h*( 64) when*h*(*x*) = √*x*– 3√*x*. - Suppose that after t seconds, a rock thrown off a bridge has height
*s*(*t*) = –16*t*^{2}+ 20*t*+ 100 feet off the ground. How high is it after 3 seconds? - Suppose that the profit on making and selling
*x*cookies is . How much profit is made on 100 cookies?

**Simplify the following.**

*f*(*y*) when*f*(*x*) =*x*^{2}+ 3*x*– 1*f*(*y*+ 1) when*f*(*x*) =*x*^{2}+ 3*x*– 1*f*(*x*+*a*) when*f*(*x*) =*x*^{2}+ 3*x*– 1*g*(*x*^{2}+ √*x*) when*g*(2*x*) –*g*(*x*) when*f*(*x*+*a*) –*f*(*x*) when*f*(*x*) =*x*^{2}+ 4*x*– 5- when
*h*(*x*) = 3*x*+ 2 - when
*g*(*x*) =*x*^{2}– 2*x*+ 1

**Using g(x) = x^{3} – 2x^{2} + 1, and h(x) = x – √x, simplify the following compositions.**

*f**g*(*x*)-
*g**f*(*x*) *f**h*(*t*)*f**f*(*x*)*h**h*(*x*)*g**h*(9)*h**f**g*(*x*)-
*f**h**f*(2*x*)

**Find the domain of each of the following functions.**

**26.***h*(*x*) = √*x*+1*g*(*x*) =*x*^{2}+ 5*x*– 6*h*(*x*) =^{3}√*x*

**Solutions**

*f*(5) = 9*g*( –3) = –20*h*= 1*f*(7) = 2. Because there is no*x*in the description of*f*, the 7 never gets used. This is called a*constant*function because it is constantly equal to 2.*k*(4) = 21*h*(64) = 4- The rock is
*s*(3) = 16 feet high after 3 seconds. - The profit on 100 cookies is
*P*(100) = $39. *f*(*y*) =*y*^{2}+ 3y – 1*f*(*y*+ 1) =*y*^{2}+ 5*y*+ 3*f*(*x*+*a*) =*x*^{2}+ 2*xa*+*a*^{2}+ 3*x*+ 3*a*– 1*g*(*x*^{2}+ √*x*) = – 6(*x*^{2}+ √*x*)*g*(2*x*) –*g*(*x*) =*f*(*x*+*a*) –*f*(*x*) = (*x*+*a*)^{2}+ 4(*x*+*a*) – 5 – (*x*^{2}+ 4*x*– 5) = 2*xa*+*a*^{2}+ 4*a*- = 2
*x*+*a*– 2 -
*g**h*(9) =*g*(9 – √9) =*g*(6) = 145 *h**f**g*(*x*) =*h*(*f*(*g*(*x*))) =*f**h**f*(2*x*) =*x*≠ – 3,*x*≠ 5*x*≥ –1*t*> –5 because*t*≠ –5- The domain consists of all real numbers.
*a*≠ 0- The domain consists of all real numbers.
*x*≤ 2,*x*≠ – 8*u*> is enough, because it already rules out*u*≠ –3 and*u*≠ .

From Calculus Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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