Question

If f(x) = 2x - 1 and g(x) = x^2 - 2, find [g · f](x) please show me how to do this

Answer 1

Answer:

(x² -7)/(2x + 1)

Step-by-step explanation:

f(x) = 2x+1 and g(x) = x² -7

thus: (g/f)(x) = g(x)/f(x) = x² -7/2x + 1

Answer 2

Hello!

The answer is:

$(g \circ f)(x)=4x^{2}-4x-1$

Why?

To solve the problem, we need to remember that composing functions means evaluate a function into another different function.

Also, we need to remember how to solve the following notable product:

$(a-b)^{2}=a^{2}-2ab+b^{2}$

We have that:

$(g \circ f)(x)=g(f(x))$

Now, we are given the equations:

$f(x)=2x-1\\g(x)=x^{2}-2$

So, composing we have:

$(g \circ f)(x)=g(f(x))$

$(g \circ f)(x)=(2x-1)^{2}-2$

Now, we have to solve the notable product:

$(g \circ f)(x)=((2x)^{2}-2(2x*1)+1^{2})-2$

$(g \circ f)(x)=4x^{2}-4x+1-2$

Hence, we have that:

$(g \circ f)(x)=4x^{2}-4x-1$

Have a nice day!