Question

Help, will medal and fan if givin correct answer !
1
If f(x) = x2 and g(x) = ----- , find g(f(-1)).
2x + 3

Answer 1

start by finding f(-1) which requires you to substitute x = -1 into f(x)

then when you get a number answer substitute it into g(x)

Answer 2

no needs for medals, all I need is some effort on your behalf:)
I will give you a similar example: g(f(-2))

\(\large\color{black}{ f(x)=x^3 \\g(x)=\frac{\LARGE 1}{\LARGE 3x+4} }\)

\(\large\color{black}{ g(\color{red}{f(x)})=\frac{\LARGE 1}{\LARGE 2\color{red}{(x^3)}+3} }\)

\(\large\color{black}{ g(\color{red}{f(x)})=\frac{\LARGE 1}{\LARGE 2x^3+3} }\)

\(\large\color{black}{ g(\color{red}{f(\color{blue}{-2})})=\frac{\LARGE 1}{\LARGE 2(\color{blue}{-2})^3+3} }\)

\(\large\color{black}{ g(\color{red}{f(\color{blue}{-2})})=\frac{\LARGE 1}{\LARGE 2(-8)+3} }\)

\(\large\color{black}{ g(\color{red}{f(\color{blue}{-2})})=\frac{\LARGE 1}{\LARGE -16+3} }\)

\(\large\color{black}{ g(\color{red}{f(\color{blue}{-2})})=\frac{\LARGE 1}{\LARGE -13} }\)

Answer 3

So my answr is either 1 or -1 ?

Answer 4

no

Answer 5

~ plug in x^2 instead of x, into the g(x).
~ plug in "-1" instead of x. (once you perform the first step)
~ simplify the denominator.

what do you get>?

Answer 6

well look at it this way

f(-1) = (-1)^2

so what value does f(-1) take..?

Answer 7

i dont konow, im good at math but this stuff confuses me. im nly n 9th grade

Answer 8

well all you are being asked to do is square negative 1...

so

f(-1) = -1 x -1

what do you think the answer is..?

Answer 9

multiply them ?

Answer 10

yes

Answer 11

what answer did you get..?

Answer 12

1

Answer 13

great now this value of substituted into g(x)

so f(x) = 1

\[g(1) = \frac{1}{2 \times 1 + 3}\]

what answer do you get..?