How do you find $(f o g) (x)$ $(fog)(x)$ given $f (x) = 2 x - 5$ $f(x)=2x-5$ and $g (x) = x + 2$ $g(x)=x+2$ ?

Question

11568 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-16T14:25:11

$(f o g) (x) = 2 x - 1$ $(fog)(x)=2x-1$

Another way of looking at it:

set $g(x)->y_1=x+2...........Equation(1)$

set $f(x)->y_2=2x-5........Equation(2)$

$(fog)(x)$ is such that as f is before the g in $(fog)(x)$

so wherever in $f(x)$ you see $x$ you substitute $y_1$ That is; you are substituting $Equation(1)$ into any $x" that is in "Equation(2)$

So: $(fog)(x)=color(green)(2(color(red)(y_1))-5)$

but $" "color(red)(y_1=x+2)$

So: $(fog)(x)=color(green)(2(color(red)(x+2))-5)$

$(fog)(x)=2x+4-5" "=" "2x-1$

How do you find (fog)(x)(fog)(x)(fog)(x) given f(x)=2x-5f(x)=2x−5f(x)=2x-5 and g(x)=x+2g(x)=x+2g(x)=x+2?