Given that $f(x)=x^2-4x$ and $g(x)=x+3$ , what is $(f∘g)(1)$ ?

Question

9179 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-22T15:45:04

$(f@g)(1) = 0$

The notation $(f @ g)(x)$ means the same thing as $f(g(x))$ , or to insert $g(x)$ as the $x$ values of $f(x)$ .

The $1$ that replaces the $x$ means that we just need to calculate the value at the end by substituting $1$ for $x$ inside the new-formed function.

$(f@g)(x) = (x + 3)^2 - 4(x + 3) = x^2 + 6x + 9 - 4x - 12 = x^2 + 2x - 3$

If you want it in factored form, we can say it is equal to $(x + 3)(x -1)$ .

Now, $(f@g)(-1) = (1 + 3)(1 - 1) = 0$ .

Hopefully this helps!

Given that f(x)=x^2-4xf(x)=x^2-4x and g(x)=x+3g(x)=x+3, what is (f∘g)(1)(f∘g)(1)?