F(x) + 7 =? I need help.

Question

Let f(x) = 2x ^ 2 + 2 Express the following function values in terms of x.

f(x)+ 7 =?

Answer 1

Heya Zam.

When an equation is written in function notation like in the question, you want to calculate things inside of parentheses before you calculate the other parts, similar to arithmetic.

In arithmetic for example, 5 × (2 + 1) = 5 × (3) = 15.

You calculate the things inside the parentheses first, then you can calculate the rest.

We want to use the same idea for a function.

Let's take a very simple function g(x) = 2x. The letter chosen for functions can be anything, usually starts from f and going down the alphabet, in the same way that with variables, it can be any letter, but usually starts at x, and then y, etc.

With this function g(x), let's calculate two things and see what the outcomes look like.

g(x + 1)

g(x) + 1

As I mentioned above, we want to calculate things inside the parentheses first, then the rest.

With functions, the way to calculate something inside the parentheses is to substitute whatever is in the parentheses into x in the function.

Here are some examples for how that would work with different things in the parentheses:

g(x) = 2x

g(y) = 2y

g(5) = 2(5) = 10

g(x + 1) = 2(x + 1) = 2x + 2

Whatever was inside the parentheses, that whole thing is substituted for x and then the equation can be simplified.

Great, now we want to know how to calculate things outside of the parentheses. For those, we just calculate them after everything in the function has been done.

Here are some examples for calculating different things outside the parentheses:

g(x) = 2x

g(x) × 2 = 2(x) × 2 = 4x

g(x) + 1 = 2(x) + 1 = 2x + 1

As you can see, the effect of having something inside or outside the parentheses changes the final result, even though all the elements of the two are the same.

g(x + 1) = 2x + 2

g(x) + 1 = 2x + 1

Going further, we can also combine the two. We can have a calculation inside the parentheses and one outside. Like always, we want to calculate the stuff inside first.

g(x) = 2x

g(x + 1) + 1 = ( 2(x+1) ) + 1 = 2x + 2 + 1 = 2x + 3

Using this information, the question should be quite simple to solve.

Hope that was helpful. Let me know if you have any other questions.

Answer 2

f(x) = 2x^2 + 2

f(x) + 7 = 2x^2 + 2 + 7 = 2x^2 + 9