Plug 5 into first:

Now, plug this answer into :

Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x² – 12) + 7.

Distribute the 3: 3x² – 36 + 7 = 3x² – 29

The correct answer is 29. We plug in 3 into the equation above and solve for x. So we find that f(x) = 4(3) + 17. 12 + 17 = 29

It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).

Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

The correct answer is 4 because 

F(x) = 2x + 3^x + (9x/3) = 2(4) + 3⁴ + ((9 * 4)/3) = 101, and

G(x) = (((2⁴ + 4⁴)/2) - 4 * 4) – 5(4) + 1 = 101.  

Substitute -1 for  in the given function.

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that  is 1, then you will have calculated 18.

We can take each of the listed transformations of  one at a time. If  is to be shifted up by four units, increase every value of  by 4. 

Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So,  can be written in the following way:

Lastly, distribute the negative sign to arrive at the final answer.

The range of a function is the set of y-values that a function can take. First let's find the domain. The domain is the set of x-values that the function can take. Here the domain is all real numbers because no x-value will make this function undefined. (Dividing by 0 is an example of an operation that would make the function undefined.)

So if any value of x can be plugged into y = x² + 2, can y take any value also? Not quite! The smallest value that y can ever be is 2. No matter what value of x is plugged in, y = x² + 2 will never produce a number less than 2. Therefore the range is y ≥ 2.

Values of x that make the denominator equal zero are not included in the domain. The denominator can be simplified to (x – 3)², so the value that makes it zero is 3.

The domain of a relation is the same as the range of the inverse of the relation.  In other words, the x-values of the relation are the y-values of the inverse.

The range of a function is the set of y-values that a function can take. First let's find the domain. The domain is the set of x-values that the function can take. Here the domain is all real numbers because no x-value will make this function undefined. (Dividing by 0 is an example of an operation that would make the function undefined.)

So if any value of x can be plugged into y = x² + 2, can y take any value also? Not quite! The smallest value that y can ever be is 2. No matter what value of x is plugged in, y = x² + 2 will never produce a number less than 2. Therefore the range is y ≥ 2.