Question

If f(x)=x^2 and g(x)=1÷2x+3 find g(f(-1))

Answer 1

`g(f( - 1)) = (1)/(5 )`

Step-by-step explanation

The given function is:

`f(x) = {x}^(2)`

and

`g(x) = (1)/(2x + 3)`

`g(f(x)) = g( {x}^(2) )`

`g(f(x)) = \frac{1}{2{x}^(2) + 3 }`

To find g(f(-1)), we substitute x=-1, to obtain;

`g(f( - 1)) = \frac{1}{2{( - 1)}^(2) + 3 }`

We simplify the square in the denominator to get,

`g(f( - 1)) = (1)/(2+ 3 )`

We now add the denominator to obtain;

`g(f( - 1)) = (1)/(5 )`