Question

What is the range of this function? F(x)=3/x+4 + 1

Answer 1

Answer: the range of the function f(x) = 3/(x+4) + 1 is (-∞, 1) U (1, +∞), which means that the function can output any real number except 1.

Explanation:

To determine the range of the function f(x) = 3/(x+4) + 1, we need to consider the possible output values of the function for different input values of x.

1. Start by analyzing the domain of the function. In this case, the function is defined for all real numbers except x = -4, since division by zero is undefined.

2. As x approaches -4 from the left side, the function approaches negative infinity. As x approaches -4 from the right side, the function approaches positive infinity.

3. As x becomes very large (positive or negative), the function approaches a value of 1. This can be seen by considering the behavior of the function as x gets larger and larger.

4. Therefore, the range of the function is all real numbers except 1. In interval notation, the range can be expressed as (-∞, 1) U (1, +∞).

To summarize, the range of the function f(x) = 3/(x+4) + 1 is (-∞, 1) U (1, +∞), which means that the function can output any real number except 1.

I hope this helps :)

Answer 2

(−∞,1)∪(1,∞)

Explanation:

The range of a function is the set of all possible output values of the function.

In other words, it is the set of all y values that can be obtained by evaluating the function for some input value x.

To find the range of
`\sf F(x)=(3)/(x+4)+1`, we can first rewrite it as:

`\sf F(x)=(3+x+4)/(x+4)`

We can see that the denominator of F(x) is never equal to zero, so F(x) is defined for all real numbers x.

Therefore, the range of F(x) is all real numbers y except for 1.

In other words, the range of F(x) is:

y≠1

This can also be written in interval notation as:

(−∞,1)∪(1,∞)