# Thread: slope : tangent

1. ## slope : tangent

If f(x)=5/(x^2+1) and g(x)=3x, then g(f(2))= ?

i just need someone to reminde me about the substitution process.

is it like... 5/[(3x)^2+1] or 3[5/(x^2+1)]

2. Originally Posted by DINOCALC09
If f(x)=5/(x^2+1) and g(x)=3x, then g(f(2))= ?

i just need someone to reminde me about the substitution process.

is it like... 5/[(3x)^2+1] or 3[5/(x^2+1)]
the second one

3. Originally Posted by DINOCALC09
If f(x)=5/(x^2+1) and g(x)=3x, then g(f(2))= ?

i just need someone to reminde me about the substitution process.

is it like... 5/[(3x)^2+1] or 3[5/(x^2+1)]
g(f(x)) means you take the function f and plug it into g. just like how g(3) means you take the number 3 and plug it into g...same concept, only you're plugging in a function, not a number.

so, $\displaystyle g(f(x)) = 3(f(x)) = 3 \left( \frac 5{x^2 + 1} \right) = \frac {15}{x^2 + 1}$

however, with these computational questions, i think it's easier to evaluate f(2) and then plug that number into g. it's usually easier that way...to me