Question

Let f(x)=5x and g(x)=25x^2/sqrt 5(x-2)

Answer 1

Write g(x) in terms of f(x)

Answer 2

f(x) = 5x

divide 5 both sides
f(x)/5 = x

which is same as
x = f(x)/5

Answer 3

plug that in g(x) in place of "x" everywhere

Answer 4

can you help me

Answer 5

write down g(x) first :
\[g(\color{blue}{x})=\dfrac{25\color{blue}{x}^2}{\sqrt{5(\color{blue}{x}-2)}}\]

Answer 6

simply replace \(\color{blue}{x}\) by \(\color{blue}{f(x)/5}\) and simplify

Answer 7

\[\begin{align}g(\color{blue}{x})&=\dfrac{25\color{blue}{(f(x)/5)}^2}{\sqrt{5(\color{blue}{f(x)/5}-2)}}\\~\\
&=\dfrac{25\color{blue}{(f(x))^2/25}}{\sqrt{\color{blue}{f(x)}-10}}\\~\\
&=\dfrac{\color{blue}{(f(x))^2}}{\sqrt{\color{blue}{f(x)}-10}}\\~\\

\end{align}\]

Answer 8

so that's the answer the last step right?

Answer 9

Yes :/

Answer 10

thank you so much(;
Can you help me with one more similar one

Answer 11

Id love to help, but if it is a similar one, I'm pretty sure you can work it on your own :)

Answer 12

give your best try

Answer 13

Please.....Let f(x) =2sqrt x and g(x)=x^2+x. Write g(x) in terms of f(x)

Answer 14

take first function :
\[f(x)=2\sqrt{x}\]

square both sides and get
\[\begin{align}(f(x))^2 &= (2\sqrt{x})^2\\~\\f(x)^2&=4x\end{align}\]

Answer 15

divide "4" both sides, what do u get ?

Answer 16

2x

Answer 17

nope try again

Answer 18

I'm sorry i can't seem to do it

Answer 19

thats okay, let me show u how to do it this one time
We have :
\[\begin{align}f(x)^2&=4x\end{align}\]

Dividing "4" both sides :
\[\begin{align}\frac{f(x)^2}{4}&=\frac{4x}{4}\end{align}\]

On right hand side, we can cancel "4" top and bottom and get
\[\begin{align}\frac{f(x)^2}{4}&=x\end{align}\]

Answer 20

which is same as
\[x = \dfrac{f(x)^2}{4}\]

Answer 21

plug that in g(x) in place of "x" everywhere
simplify

Answer 22

\[\begin{align} g(\color{blue}{x})&=\color{blue}{x}^2+\color{blue}{x}\\~\\
&=\left(\color{blue}{\frac{f(x)^2}{4}}\right)^2+\color{blue}{\frac{f(x)^2}{4}}\\~\\
&=\color{blue}{\frac{f(x)^4}{16}} + \color{blue}{\frac{f(x)^2}{4}}\\~\\
\end{align}\]

Answer 23

so that's the answer right? @ganeshie8