Question

If q(x)=5-x^2 and p(q(x))=4-x^2/x^2 when x is not equal to zero, then what is p(1/4) equal to?

can you explain the answer when your answer?

Answer 1

`p(1/4)=-3/19`

Explanation:

As `q(x)=5-x^2` and `p(q(x))=(4-x^2)/x^2`

As we are using `x^2` in latter function, we get the value of `x^2` from first function i.e. `q(x)=5-x^2`

and we get `x^2=5-q(x)`

Then `4-x^2=4-(5-q(x))=4-5+q(x)=q(x)-1`

and `x^2=5-q(x)`

Hence `p(q(x))=(4-x^2)/x^2=(q(x)-1)/(5-q(x))`

and `p(x)=(x-1)/(5-x)` and `p(1/4)=(1/4-1)/(5-1/4)`

= `(-3/4)/(19/4)=-3/4xx4/19=-3/19`