FUNCTION COMBINATION IN MATH

Posted by : Allan_Dell on Thursday, May 31, 2018 | 1:27 AM

FUNCTION COMBINATION

In calculus, most functions involved are combinations of functions. We can combine functions like f-g(x) for subtraction, f+g(x) for addition, f*g(x) for multiplication, and f/g (x) and for division.

Many of the students especially those who are not in a "constant practice" as a model for math learning found this complicated. To make it more fun, examples are provided to make the information clear.

Illustrations:

Find $f\ o\ g(x)\ {\color{Red} and}\ g\ o\ f(x)$ , If:

$a) f(x)=x-1\and\ g(x)=x+1$

$b.) f(x)=x^{2}-1\and\ g(x)=2x^{2}-2$

$c.) f(x)=3x-1\and\ g(x)=x^{2}-4$

$d.)f(x)=x^{2};g(x)=3-x^{2}$

$e.)f(x)=\sqrt{x-2};g(x)=x^{2}$

Solution:

$a.) fog(x)=f[g(x)]=f[(x+1)]=[(x+1)-1]=[x+1-1]=x$

$g o f(x)=g[f(x)]=g[x-1]=[(x-1)+1]=[x-1+1]=x$

$b.)fog(x)=f[g(x)]=f[2x^{2}-2]=[(2x^{2}-2)^{2}-1]=4x^{2}-8x^{2}+4-1$

$={\color{Red} 4x^{2}-8x^{2}+3}$

$gof(x)=g[f(x)]=g[x^{2}-1]=2(x^{2}-1)^{2}-2=2(x^{4}-2x^{2}+1)-2$

$={\color{Red} 2x^{4}-4x^{2}+2}$

$c.)fog(x)=f[g(x)]=f[x^{2}-4]=3(x^{2}-4)-1=3x^{2}-12-1={\color{Red} 3x^{2}-13}$

$gof(x)=g[f(x)]=g[3x-1]=(3x-1)^{2}-4={\color{Red} 9x^{2}-6x-3}$

$d.)fog(x)=f[g(x)]=f[3-x^{2}]=[3-(x^{2})^{2}]={\color{Red} 3-x^{4}}$

$gof(x)=g[f(x)]=g(x^{2})=(3-x^{2})^{2}={\color{Red} 9-6x^{2}+x^{4}}$

$e.)fog(x)=f[g(x)]=f[x^{2}]={\color{Red} \sqrt{x^{2}-2}}$

$gof(x)=g[f(x)]=g[\sqrt{x-2}]=(\sqrt{x-2})^{2}={\color{Red} x-2}$

More Examples:

Find fog(-2), fog(0), and gof(-3) for :

$f(x)=3x+2, {\color{Red} and} \ g(x)= 1-x^{2}$

Solution for fog(-2):

$First,compute\ g(-2)$

$g(x)=1-x^{2}$

$g(-2)=1-(-2)^{2}=1-4={\color{Red} -3}$

$Now, evalutef(x)@x=-3$

$fog(-2)=f[g(-2)]=f(-3)=3(-3)+2=-9+2={\color{Red} -7}$

Solution for fog(0):

$First,compute\ g(0)$

$g(x)=1-x^{2}$

$g(0)=1-x^{2}=1-(0)^{2}={\color{Red} 1}$

$Now, evaluatef(x)@x=1$

$fog(0)=f[g(0)]=f[1]=3(1)+2={\color{Red} 5}$

Solution for gof(-3):

$First,compute\ f(-3)$

$f(x)=3x+2$

$f(-3)=3(-3)+2=-9+2={\color{Red} -7}$

$Now,evaluate\g(x)@x=-7$

$gof(x)=g[f(x)]=g[1-x^{2}]=[1-(-7)^{2}]=1-49={\color{Red} -48}$

Challenge yourself:

Given the following functions, write your answer on the "Post a Comment" box below this page.

$Given \ a\ function\ f(x)=2x-1, find;$

$a.)f(-2)$ , click for your answer

$b.)f(2a)$ , click for your answer

$c.)f(a+1)$ , click for your answer

I know, b and c are the hard ones!

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DMG

FUNCTION COMBINATION IN MATH

Posted by : Allan_Dell on Thursday, May 31, 2018 | 1:27 AM

FUNCTION COMBINATION

Illustrations:

Solution:

More Examples:

Solution for fog(-2):

Solution for fog(0):

Solution for gof(-3):

Challenge yourself:

Popular posts

DMG

FUNCTION COMBINATION IN MATH

Posted by : Allan_Dell on Thursday, May 31, 2018 | 1:27 AM

FUNCTION COMBINATION

Illustrations:

Solution:

More Examples:

Solution for fog(-2):

Solution for fog(0):

Solution for gof(-3):

Challenge yourself:

Popular posts

Posted by : Allan_Dell on Thursday, May 31, 2018 | 1:27 AM