Prove that f(x)=x+3/2 and g(x)=2x-3 are inverses

Mathematics

2 answers:

sergeinik [125]4 years ago

8 0

Yes yyou are absolutely correct!^

polet [3.4K]4 years ago

7 0

That means, F(x) · g(x)=1
(X+3/2) · (2X-3)=1
2X-3=2(X-3/2)
If the X= + or - √11/2
Then the <span>f(x)=x+3/2 and g(x)=2x-3 are inverses.</span>

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What is 04.151515... into a fraction

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)