Question

find th domain and range of f(X) = 1/cos(logx)​

Answer 1

Answer:

Domain :- x > 0 excluding $e^{\frac{\pi}{2}}$

Range :- x belongs to [ $-\infty$ , -1 ]U [ $1\:,\infty$ ]

Step-by-step explanation:

• For domain ,we have to refer to the definition of log(x).It should be x > 0.

• Also,cos(logx) should not be zero as this would lead to an indefinite value.That is why ,we will exclude that x which gives cos(logx) = 0.

cos(logx) = 0

=> logx = π/2

=> x = $e^{\frac{\pi}{2}}$

Therefore,domain would be x > 0 excluding $e^{\dfrac{\pi}{2}}$.

• Range is the value a function can take.

• Here,cos(logx) can take values from [-1,1].

• Therefore,its reciprocal can take values from [ $-\infty \:,-1$ ] U [ $1\:,\infty$ ].