Mathematics: If f(x)=x-6/x and g(x)=x+4 and h(x)=3x-2 what is h(f(g(

Sum the number you get when you add two numbers. It also means a particular amount of money....

If f(x)=x-6/x and g(x)=x+4 and h(x)=3x-2 what is

Jinesha

26.05.2020

The answer is h(f(g(x))) = $\frac{3*(x+4)^{2}-6 }{x+4} -2$

Step-by-step explanation:

Given f(x)= x-6/x

g(x) = x+4

h(x) =3x-2

We have to find h(f(g(x))) ?

Basically it is a composite function i.e.

function within a function

So now f(g(x))=f(x+4)

i.e. we are going to put x+4 in place of g(x)

f(g(x))= x+4 - $\frac{6}{x+4}$

Multiplying both sides by x+4

f(g(x)) *x+4=(x+4) $(x+4)^{2}$ -6

Now dividing both sides by x+4

f(g(x)) = $\frac{((x+4)^{2}-6 }{x+4}$ /(x+4)

Now h(f(g(x)))= h( $\frac{(x+4)^{2}-6 }{x+4}$ )

=3( $\frac{(x+4)^{2}- 6 }{x+4}$ -2

Multiplying both sides by x+4

h(f(g(x)) *(x+4) =3* $(x+4)^{2}$ -6 -2*(x+4)

Now dividing both sides by (x+4)

h(f(g(x)) =3* $\frac{3*(x+4)^{2} )-6}{x+4}$ -2

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