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Find the domain of f(x)=sqrt((0. 625)^(4...

Find the domain of `f(x)=sqrt((0. 625)^(4-3x)-(1. 6)^(x(x+8)))`

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Clearly, `(0.625)^(4-3x)ge(1.6)^(x(x+8))`
or `((5)/(8))^(4-3x) ge ((8)/(5))^(x(x+8))`
or `((8)/(5))^(3x-4) ge ((8)/(5))^(x(x+8))`
or `3x-4 ge x^(2)+8x " or " x^(2) +5x +4 le 0`
or `-4 le x le -1`
Hence, the domain of function `f(x)` is `x in [-4,-1].`
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