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# composite functions

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f(x)=3x-2

g(x)=10/x+2

a) express the inverse function f^-1 in the form f^-1(x)

b) find gf(x)

simplify your answer

lynx7  Feb 24, 2018

### Best Answer

#1
+6536
+2

a)

f(x)   =   3x - 2       Instead of  " f(x) "  let's say  y .

y  =  3x - 2            Now let's solve this equation for  x .

Add  2  to both sides.

y + 2  =  3x

Divide both sides by  3 .

(y + 2)/3  =  x

So the inverse function is....

f-1(x)  =  (x + 2)/3

b)   I guess that this means find  (g o f)(x) .

(g o f)(x)  =  g( f(x) )

(g o f)(x)  =  g( 3x - 2 )

(g o f)(x)  =  10/( 3x - 2 ) + 2

hectictar  Feb 24, 2018
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### 1+0 Answers

#1
+6536
+2
Best Answer

a)

f(x)   =   3x - 2       Instead of  " f(x) "  let's say  y .

y  =  3x - 2            Now let's solve this equation for  x .

Add  2  to both sides.

y + 2  =  3x

Divide both sides by  3 .

(y + 2)/3  =  x

So the inverse function is....

f-1(x)  =  (x + 2)/3

b)   I guess that this means find  (g o f)(x) .

(g o f)(x)  =  g( f(x) )

(g o f)(x)  =  g( 3x - 2 )

(g o f)(x)  =  10/( 3x - 2 ) + 2

hectictar  Feb 24, 2018

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