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Thread: Simplifying Expressions

  1. #1
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    Simplifying Expressions

    How would simplify this? I can't seem to get the right answer.

    For the function f(x)=x^2−7x, simplify each expression as much as possible.

    1) (f(x+h) - f(x)) / h :h cannot = 0

    and 2) (f(w) - f(x)) / w - x :x cannot = w
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  2. #2
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    Have you at least tried to evaluate $\displaystyle f(x + h)$?
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  3. #3
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    Sadly i don't know how to even go about that. Since h has no defined statement, would i just leave it as the variable h? So would that turn into (x^2 -7x +h) - (x^2 - 7x) and then the x^2's and the 7x's would cancel out and i would be left with just h?
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  4. #4
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    Replace each $\displaystyle x$ in $\displaystyle f(x)$ with $\displaystyle x + h$.
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  5. #5
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    (x+h)^2 - 7(x+h) => (x^2 + h^2 +2hx) - (7x+h)

    Like this?
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  6. #6
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    Yes, and you can simplify it further.

    Then evaluate $\displaystyle f(x + h) - f(x)$.

    Then evaluate $\displaystyle \frac{f(x +h) - f(x)}{h}$.
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  7. #7
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    So now i have x^2 + h^2 - 5hx / h. How can i simplify this further?
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  8. #8
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    Check your simplification of $\displaystyle f(x + h) - f(x)$ again. Each term should have an $\displaystyle h$ in it.
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  9. #9
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    I don't see it. How would you end up with a h in the x^2 term?
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  10. #10
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    $\displaystyle f(x + h) - f(x) = (x^2 + 2xh + h^2 - 7x - 7h) - (x^2 - 7x)$

    $\displaystyle = 2xh + h^2 - 7h$.


    So what do you think $\displaystyle \frac{f(x+h)-f(x)}{h}$ is?
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  11. #11
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    Would you divide out h? so you would be left with 2x + h -7. Would i isolate h to leave 7 - 2x?
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  12. #12
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    Yes, divide everything by $\displaystyle h$. So the first thing you wrote is correct.
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  13. #13
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    What would i do next? Since i am not allowed to have an h in my answer.
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  14. #14
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    Why can't you keep an $\displaystyle h$ in your answer? All you've been told is that $\displaystyle h \neq 0$...
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  15. #15
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    If i enter an answer with h in it it prompts me saying that i cannot have an h.
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