Question

Let f(x) = x + 3 and g(x) = 1/x The graph of (gºf)(x) is shown below what is the range of ( gof) (x) .

Answer 1

Answer:

The range of the function $(g\°f)(x)$ is

B.  is all real numbers except $y=0$

Step-by-step explanation:

Given functions:

$f(x)=x+3$

$g(x)=\frac{1}{x}$

To find the range of $(g\°f)(x)$.

Solution:

In order to find $(g\°f)(x)$ , we will plugin $f(x)$ in function $g(x)$.

$(g\°f)(x)=g(f(x))$

$(g\°f)(x)=\frac{1}{x+3}$

The graph of the function $(g\°f)(x)$ shows that

1) As $x$ approaches -3 (but never touches the line $x=-3$), $y$ tends to positive or negative infinity.

2) As $y$ approaches 0 (but never touches the line $y=0$) , $x$ tends to positive or negative infinity.

Thus, the range of the function is all real numbers except $y=0$