Question

Match each of the functions on the left with the correct rule on the right?

Answer 1

The functions are f(x) = 10/x and g(x) = x /(x + 10)

(fog)(x) = f(g(x))

Substitute the expression for functioning g (in this case x /(x + 10) ) for g(x) in the composition.

= f[x /(x + 10)]

Now substitute this expression (x /(x + 10)) in to function f in place of the x value.

= 10/[x /(x + 10)]

= 10(x + 10)/x

(fog)(x) = H

 

(gof)(x) = g(f(x))

Substitute the expression for functioning f (in this case 10/x) for f(x) in the composition.

= g(10/x)

Now substitute this expression (10/x) in to function g in place of the x value.

= (10/x)/[(10/x) + 10)]

= (10/x)/[(10+10x)/x]

= 10/(10 + 10x)

= 1/(1 + x)

(gof)(x) = C

 

(fof)(x) = f(f(x))

Substitute the expression for functioning f (in this case 10/x) for g(x) in the composition.

= f(10/x)

Now substitute this expression (10/x) in to function f in place of the x value.

= 10/(10/x)

= 10x/10

= x

(fof)(x) = E

 

(gog)(x) = g(g(x))

Substitute the expression for functioning g (in this case x /(x + 10)) for f(x) in the composition.

= g[x /(x + 10)]

Now substitute this expression (x /(x + 10)) in to function g in place of the x value.

= [x /(x + 10)]/{[x /(x + 10)]+10}

= [x /(x + 10)]/[(x+10x+100) /(x + 10)]

= x/(11x+100)

(gog)(x) = G.