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Find the number of solutions to 7^|x|(|1...

Find the number of solutions to `7^|x|(|1-|x||)=1`.

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We have `7^|x|(|1-|x||)=1`
or `|1-|x||=7^(-|x|)`
To find the number of solutions to the equation, we draw the graph of `y=|1-|x||andy=7^(-|x|)` and find number of points of intersection. The graphs of both the functions are as intersection.
The graphs of both the functions are as shown in the following figure.

From the graph, the number of solutions is 5.
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CENGAGE-GRAPHICAL TRANSFORMATIONS-Exercise
  1. Find the number of solutions to 7^|x|(|1-|x||)=1.

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  2. Draw the graph of y=tan^(-1)x-cot^(-1)x.

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  3. Draw the graph of y=|(1)/(|x|)-2|.

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  4. Draw the graph of y=tan^(-1)x+cos^(-1)x+sin^(-1)x.

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  5. Draw the graph of |y|=(x-1)(x-2)(x-3).

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  6. Draw the graph of y=2sin^(-1)(x//3).

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  7. Draw the graph of y=cot^(-1)|x|.

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  8. Draw the graph of y=sec^(-1)|x|.

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  9. Draw the graph of y=|log(e)(x+3)|.

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  10. Draw the graph of y=|log(e)|x||.

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  11. Draw the graph of y=|{x}-0.5|, where {.} represents the fractional par...

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  12. Draw the graph of y=|sinx|+sin|x|.

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  13. If the graph of y=|f(x)| is as shown in figure then the graph of y=f(...

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  14. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  15. Find the number of real solutions to the equation log(0.5)|x|=2|x|.

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  16. Find the number of points where the function f(x)=max|tanx|,cos|x|) is...

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  17. Find the number of points of non-diferentiability for f(x)=max{||x|-1|...

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  18. Let f(x) = max. {|x^2 - 2| x ||,| x |} then number of points where f(x...

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  19. Draw the graph of |y|=[x], where [.] represents the greatest integer f...

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  20. Draw the graph of |2x|+|y|=2 using graphical transformation.

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  21. Consider the function f(x)={2x+3, x le 1 and -x^2+6, x > 1 Then draw t...

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