Question

Let f(x) = 1/x-4 and g(x) = 1/x -3, evaluate the following. a. f(1/4) =b. g(1/4)= c. f(-1/3)=d. g(-1/3)=

Answer 1

We are given the following two functions

`\begin{gathered} f(x)=(1)/(x-4) \\ g(x)=(1)/(x)-3 \end{gathered}`

Let us evaluate the functions on the given points.

a. f(1/4)

Substitute x = 1/4 into the function f(x)

`f((1)/(4))=(1)/((1)/(4)-4)=(1)/((1-4\cdot4)/(4))=(1)/((1-16)/(4))=(1)/((-15)/(4))=-(4)/(15)`

Therefore, f(1/4) = -4/15

b. g(1/4)

Substitute x = 1/4 into the function g(x)

`g((1)/(4))=(1)/((1)/(4))-3=4-3=1`

Therefore, g(1/4) = 1

c. f(-1/3)

Substitute x = -1/3 into the function f(x)

`f(-(1)/(3))=(1)/(-(1)/(3)-4)=(1)/((-1-3\cdot4)/(3))=(1)/((-1-12)/(3))=(1)/((-13)/(3))=-(3)/(13)`

Therefore, f(-1/3) = -3/13

d. g(-1/3)

Substitute x = -1/3 into the function g(x)

`g(-(1)/(3))=(1)/(-(1)/(3))-3=-3-3=-6`

Therefore, g(-1/3) = -6