JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

If $f(x)=\left(\dfrac35\right)^x+\left(\dfrac45\right)^x-1$ , $x\in\mathbf R$ , then the equation $f(x)=0$ has :

no solution

one solution

two solutions

more than two solutions

Answer and worked solution

Official answer: B

$g(x)=\left(\frac35\right)^x+\left(\frac45\right)^x$ is strictly decreasing, and $g(2)=\frac9{25}+\frac{16}{25}=1$ . So $f(x)=0$ has exactly one solution, $x=2$ .

Topics:Monotonicity Graphs of functions

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 74