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If f:R^(+)rarrA, where A={x:-5ltxltoo} i...

If `f:R^(+)rarrA`, where `A={x:-5ltxltoo}` is defined by f(x) = `x^(2)` - 5 and if
`f^(-1)(13)={-lambdasqrt((lambda-1)),lambdasqrt((lambda-1))}`, the value of `lambda` is

Text Solution

Verified by Experts

The correct Answer is:
3
`f^(-1)(13)={x:f(x)=13}={x:x^(2)-5=13}`
`={x:x^(2)=18}={x:x=pm3sqrt(2)}`
`={-3sqrt(2),3sqrt(2)}`
`={-lambdasqrt((lambda-1)),lambdasqrt((lambda-1))}" [given]"`
`therefore lambda = 3`
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