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sweet-ann [11.9K]
3 years ago
15

If f(x)=2x-3/5 , which of the following is the inverse of f(x)?

Mathematics
1 answer:
grigory [225]3 years ago
5 0

Answer:

(5x+3)/2

Step-by-step explanation:

f(x)=(2x-3)/5

f(x)=y

y=(2x-3)/5

interchanging role of x and y

x=(2y-3)/5

5x=2y-3

5x+3=2y

y=(5x+3)/2

the inverse if f(x) = (5x+3)/2

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\displaystyle\\&#10;1 \frac{2}{5} +\Big(-5 \frac{1}{2} \Big) = ? \\  \\ &#10;1 \frac{2}{5} = \frac{1\times 5+2}{5}=\boxed{\frac{7}{5}} \\  \\ &#10;-5 \frac{1}{2} =-5 -\frac{1}{2} = \frac{-5\times2-1}{2} =\frac{-10-1}{2}=\frac{-11}{2}= \boxed{-\frac{11}{2} }\\  \\ \texttt{OR} \\  \\ &#10;-5 \frac{1}{2} = -\Big(5 \frac{1}{2} \Big)= -\Big( \frac{5\times2+1}{2} \Big)=-\Big( \frac{11}{2} \Big)= \boxed{-\frac{11}{2} }


\displaystyle\\&#10;\Longrightarrow ~~1 \frac{2}{5} +\Big(-5 \frac{1}{2} \Big) =\frac{7}{5} -\frac{11}{2} = \frac{7\times 2}{5\times 2} -\frac{11\times 5}{2\times 5} = \\  \\ &#10;= \frac{14}{10} -\frac{55}{10} = \frac{14-55}{10} =\frac{-41}{10} = -\frac{41}{10}=-\frac{40+1}{10}=\boxed{\boxed{-4\frac{1}{10}}}



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