Using functions

Question

The function g is defined as:
g:x→ a/x + b

where a and b are constants.

If g(-2)=0 and g(3)=10

Find the values of a and b.

Answer 1

Let's start by plugging in our values of x and g(x). The first hint tells us that when x is -2, g(x) = 0. So that means               0 = a/-2 + b. From this we can rearrange and we get -b = a/-2 -- > b = a/2.

 

For the next hint, we have 10 = a/3 + b. Using our first equation and replacing b with a/2, we get 10 = a/3 + a/2.

 

So, finding a common denominator we change this to 10 = 2a/6 + 3a/6 = 5a/6 = 10.     So a = 60/5= 12.

 

Since b = a/2, we have b=12/2=6.

So a = 12.

b = 6.

Answer 2

Plug in the values:

g(-2)=0 so -a/2+b=0

g(3)=10 so a/3 +b=10

 solve for a and b:

b= a/2

a/3+a/2=10

5a/6 =10

a=12

b= 6

so g(x) =12/x+6