How do you write the combined function as a composition of several functions if $f (g (x)) = \sqrt{1 - x^{2}} + 2$ $f(g(x)) = sqrt (1-x^2) +2$ ?

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How do you write the combined function as a composition of several functions if $f (g (x)) = \sqrt{1 - x^{2}} + 2$ $f(g(x)) = sqrt (1-x^2) +2$ ?

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Answer 1 · 2016-02-01T00:24:14

If I remember correctly there are many "right" ways to solve this equation. $f (g (x))$ $f(g(x))$ merely means you are plugging a function of $x$ $x$ into $g$ $g$ into $f$ $f$ with each letter being a different function.

For instance: your equation for $g$ $g$ could possibly be $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ .
After, we plug in $x$ $x$ into that equation we get the same function ( $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ ).

Next step when solving multiple step functions is to plug in your result of your first function (in our case $g$ $g$ ) into the new function ( $f$ $f$ ). This is where we need another function to get $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ into $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ $+ 2$ $+2$ .

For this step we may say $(f) = x + 2$ $(f)= x+2$ .

When we plug in $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ into our new $(f) = x + 2$ $(f)=x+2$ our result is
$\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ $+ 2$ $+2$ , the equation we needed to get to.

Another solution would be to have $(g) = 1 - x^{2}$ $(g)= 1-x^2$ and $(f) = \sqrt{x} + 2$ $(f)=sqrt(x)+2$
There are many more solution, just be creative, these are only two!

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How do you write the combined function as a composition of several functions if $f (g (x)) = \sqrt{1 - x^{2}} + 2$ $f(g(x)) = sqrt (1-x^2) +2$ ?

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How do you write the combined function as a composition of several functions if f(g(x))=√1−x2+2f(g(x)) = sqrt (1-x^2) +2?

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How do you write the combined function as a composition of several functions if $f (g (x)) = \sqrt{1 - x^{2}} + 2$ $f(g(x)) = sqrt (1-x^2) +2$ ?