270
Given:
Question:
What is the value of [tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(5)? \ }[/tex]
The Process:
The form of [tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) \ }[/tex] means that f(x) is divided by g(x).
[tex]\boxed{\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) \ } \rightarrow \boxed{ \ \frac{f(x)}{g(x)} \ }}[/tex]
Let us solve the problem.
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) = \frac{7 + 4x}{\frac{1}{2x}} \ }[/tex]
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(x) = (7 + 4x) \times \frac{2x}{1} \ }[/tex]
Thus, we get [tex]\boxed{{ \ \bigg( \frac{f}{g} \bigg)(x) = 14x + 8x^2 \ }}[/tex]
And now, we can calculate the value of [tex]\bigg( \frac{f}{g} \bigg)(5)[/tex].
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 14(5) + 8(5)^2 \ }[/tex]
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 70 + 200 \ }[/tex]
Thus, the value is 270.
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Alternative thinking
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = \frac{7 + 4(5)}{\frac{1}{2(5)}} \ }[/tex]
[tex]\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = (7 + 20) \times 10} \ }[/tex]
[tex]\boxed{\boxed{ \ \bigg( \frac{f}{g} \bigg)(5) = 270 \ }}[/tex]
Keywords: if, f(x), g(x), function, divide by, the value, (f/g)(5), 5, 270
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