Evaluating [ g(x+h) - g(x) ] / h, given g(x) = 5 - x^2

Hi, I need a little help with problems like these; could someone give me step by step instructions on solving them?

1.Given the function g(x) = 5 − x²,


2. Given the function g(x) = x² + 2x,

evaluate [g(x) − g(a)] / [x - a] , x ≠ a

I know the answer for the second one, but I don't know how to solve them, and I really want to learn as I am sure it will be on other tests.

Thank you SO mycg!!

The answer to 2 is x + a + 2 , x ≠ a

larsie13 said:

1.Given the function g(x) = 5 − x², evaluate g(x + h) − g(x), h ≠ 0
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h

Click to expand...

As you can see above, we can't directly "draw" rational expressions (i.e., algebraic fractions) at this forum. This is because the forum software removes spaces at the beginning of lines.

I have edited your post, to fix the issue quoted above, by showing two other methods.

Drawing fractions requires use of code and /code tags, to prevent consecutive spaces from being deleted (I used code tags, in your first exercise); it also helps when spacing things, to use the fixed-width font Courier New.

Alternatively, you may show rational expressions by using a slash for the fraction bar. Be sure to put grouping symbols around numerators and denominators where needed (as I did, in your second exercise).

:idea: In the Read Before Posting announcement, you can also check out the link titled, "Formatting Math as Text", to learn how to type math expressions using a keyboard. For example, we can show exponentiation using the caret symbol ^.


These sorts of exercises basically involve substitution, followed by factoring and simplification.

I know the answer for the second one …

Given the function g(x) = x^2 + 2x

evaluate [g(x) − g(a)] / [x - a] , x ≠ a

Click to expand...

You need to substitute the expression x^2+2x for g(x), in the numerator.

You need to determine the expression for g(a) and then substitute it for g(a), in the numerator.

After you have substituted expressions for g(x) and g(a) in the numerator, factor the numerator. In other words, it's possible to factor the expression x-a out of the numerator, and then it cancels with the denominator -- leaving x+a+2.

1. Given the function g(x) = 5 − x^2

evaluate [g(x + h) − g(x)] / h , h ≠ 0

Click to expand...

Same process as above.

Use the given function definition for g(x) to determine the expression for g(x+h).

Substitute this expression, and the expression for g(x), into the numerator.

Simplify the resulting numerator, and then factor it. You'll get a factor of h on the outside; it cancels with the denominator.

Show us how far you get. If you're confused about a specific step, ask us. :cool: