if h(x)=5+x and k(x)=1/x which expression is equivalent to (k×h)(x)

Question

Answer options are:

 

A).(5+x)/x

B). 1/(5+x)

C). 5+(1/x)

D). 5+(5+x)

Answer 1

Hi Garnice!

 

We all do our math differently :)  Let me show you a simple way to do this problem.

 

First of all, (K*H)(x) means that you would need to multiply the equations rather than to substitute one into the other as would be the case with something written like this K(H(x)).  SOOOO, you will need to multiply both equations.

 

K = 1/x

H = 5+x

 

K*H = 1/x(5+x)  or (5+x)1/x  which = (5+x)/x because (5+x)1/x = [(5+x)/1] * [1/x]  and anything multiplied by one is equal to itself.

 

 

normally I would also put the equation in decreased form which looks like this = 5/x + 1, however that choice is not available so the answer would be A.

 

• (5+x)1/x
• (5+x)/x
• 5/x + x/x
• because anything divided by itself is 1
• 5/x+1

 

I hope this helps!

 

Kindest regards,

Bonnie Aylor

Answer 2

Multiply: 1 (5+x) = 5 + 1

               x              x

 

1 = x

      x

 

S0, 5 + 1 = 5 + x

      x          x     x

 

So, A is your answer: (5+x)/x