Funny function

The input of the function is not $x$ . The input of the function is $\sqrt{x}$ .

Find the value of $x$ needed to make $2$ the input, i.e. set $2$ equal to $\sqrt{x}$ .

$\sqrt{x}=2\\(\sqrt{x})^{2}=2^{2}\\x=4$

To have an input of $2$ , $x$ must equal $4$ .

$f\sqrt{x})=x^{2} \\f(\sqrt{4})=4^{2}\\f(2)=16$

A change of variable might help in transforming the function: Putting $√x=X$ we get, $f(X)=X^4$ Aah! We are familiar with this form, great.

$\Rightarrow f(2)=2^4=16$

$\quad \quad \sqrt { x } =2\\ \Rightarrow \quad x\quad =4\\ \Rightarrow \quad f\left( 2 \right) ={ (4) }^{ 2 }\quad \\ \Rightarrow \quad f\left( 2 \right) =16$

Think of it as,
$f(\sqrt{x}) = x^{2}= (\sqrt{x})^{4}$ So, $f(2) = 2^{4} = \color{#0C6AC7} {\boxed {16}}$

And we're done...

Putting $x = 4$ ,

$\implies$ $f(\sqrt{4})$ = $4^2$ $\implies$ $f(2)$ = $16$

You have to make the x^2 becomes something that has the same base as square root of x. So x^2=(x^1/2)^4, then subs 2 into x^1/2, then you will get 2^4=16 Hope you guys can understand. :)

The function $f(\sqrt{x})$ is not defined for x. Thus, we need to make it into a function of a explicit input.

Assuming that $\sqrt{x}$ = t, we get $x = t^2$ . Plugging this in our function definition, $x^2=(t^2)^2=t^4$ .

Now we just need to put our value and get $2^4 = 16$ .

If it is given that f(\sqrt{x})=x^{2}

And we have, f(2)=f(\sqrt{4})=4^{2}=16

I got the answer correct and i love this society

$\Large f(\sqrt{x})=x^{2}$ $\Large =f(\sqrt{x})=((\sqrt{x})^2)^2$ $\Large =f(2)=((2)^2)^2$ $\Large =(4)^2=16$

My logic was as following, if we weren't inputed sqrt on the X we would have had a result of X to the 4th power,so, the function is powering the clean input (without square root) to the 4th power

Not sure how mathematically rigorous this is, but here is a graphical line of reasoning.

$\begin{aligned} f(\sqrt { x } ) & = & { x }^{ 2 },\quad u\overset { let }{ = } \sqrt { x } \Rightarrow x={ u }^{ 2 } \\ f(u) & = & { ({ u }^{ 2 }) }^{ 2 }={ u }^{ 4 } \\ f(2) & = & { 2 }^{ 4 }=\boxed { 16 } \end{aligned}$

so all we got to do is substitute 4 as, x^(0.5)=2 x=4. this gives us f(x)=x^2=4*4=16

$f(\sqrt(x))=x^2 \implies f(x)=x^4 \implies f(2)=2^4=\boxed{\large{16}}$

Se f(2) então x^(1/2)=2, x = 2² Assim, x = 4 f(x^(1/2)) = x², portanto f(2) = 4² f(2) = 16

substitute the value of 2 as root x,now the answer will be x square....the value of x is one and only 4so the value of x square is 16 which is the answer...

Don't BS the students. Just tell them to find, mentally, a value of x so that it's sqare root Is 2.

Can we. Do like that

If f(√x)=x^2

Then f(x)=x^4

Then x=2 so and will be 16

Please correct me if iam wrong

F(√x)=x^2 here √4 is √x so x^2=16