Given the function f(x) =3x -14, find f(3)
1 answer:
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Answer:
(2x+1)/(x^2 -4)
Step-by-step explanation:
When you add fractions (or rational expressions) you need to express each of them over a common denominator, so you can add the numerators. (Parentheses or other grouping symbols are required.)
You factor the denominator on the left so you can see what factors are missing from the denominator on the right.
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<em>Numerical example</em>
Suppose you want to add the fractions 4/15 and 3/5. You would factor the denominator 15 into 3·5, so you can see that the fraction 3/5 needs to be multiplied by (3/3) in order to give it a denominator of 15. Once the two fractions have a common denominator, you can add their numerators.
4/15 + 3/5 = 4/15 + (3/5)(3/3)
= 4/15 + 9/15
= (4+9)/15 = 13/15
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<em>Comment on grouping symbols</em>
When a rational expression is typeset, the division bar of the fraction identifies the numerator and the denominator:
When you write it in plain text as ...
x - 1/x^2 -4
this becomes a 3-term expression:
(x) -(1/x^2) -(4)
which is very different from what you may intend. In order to match the original typeset expression, parentheses must be added to show the group in the numerator and the group in the denominator:
(x -1)/(x^2 -4)
The same holds for exponents. The superscript position in a typeset expression tells you what the exponent is. When you write the same thing in plain text, parentheses are needed to show the exponent group.
= 3^(x -1) ≠ 3^x -1
That number is already in standard form.
If you need to write it in scientific notation, then do this.
<span>731,934,000
Look at all the digits that are not zero, and place the decimal point in a way that you have a number from 1 to less than 10.
Take 731934, and place the decimal point after the 7 giving 7.31934.
The original decimal point was after the third zero, so now using the original number, count the number of decimal places you moved the decimal point. The decimal point moved 8 places to the left. That means you need an exponent of 8.
</span>
If you need to write it in scientific notation, then do this.
<span>731,934,000
Look at all the digits that are not zero, and place the decimal point in a way that you have a number from 1 to less than 10.
Take 731934, and place the decimal point after the 7 giving 7.31934.
The original decimal point was after the third zero, so now using the original number, count the number of decimal places you moved the decimal point. The decimal point moved 8 places to the left. That means you need an exponent of 8.
</span>