Maths-
General
Easy
Question
Let F(
) =
, where
R. Then (F(
))–1 is equal to
- F (–
)
- F (
–1)
- F (2
)
- none of these
The correct answer is: F (–
)
We are asked to find the value of [F(α)] inverse
![F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row cell cos alpha end cell cell negative sin alpha end cell 0 row cell sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets open square brackets table row cell cos alpha end cell cell sin alpha end cell 0 row cell negative sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets
F left parenthesis alpha right parenthesis F left parenthesis negative alpha right parenthesis space equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals I
F left parenthesis negative alpha right parenthesis space equals space left square bracket F left parenthesis alpha right parenthesis right square bracket to the power of negative 1 end exponent](data:image/png;base64,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Therefore the correct option is choice 1
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