TS EAMCET · Maths · Functions
The domain of \(f(x)=\log \left[(2.5)^{3-x^2}-(0.4)^{x+9}\right]\) is
- A \((-4,3)\)
- B \((-3,4)\)
- C \((3,4)\)
- D \((0, \infty)\)
Answer & Solution
Correct Answer
(B) \((-3,4)\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=\log \left[(2.5)^{3-x^2}-(0.4)^{x+9}\right] \] \(f(x)\) is defined if \((2.5)^{3-x^2}-(0.4)^{x+9}>0\) \(\Rightarrow \quad\left(\frac{25}{10}\right)^{3-x^2}>(0.4)^{x+9}\) \(\Rightarrow \quad\left(\frac{10}{4}\right)^{3-x^2}>\left(\frac{4}{10}\right)^{x+9}\)…
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