Find the inverse of the equation y=x2+3

Mathematics

2 answers:

Veronika [31]3 years ago

5 0

Answer:

-1

f (x) = sqrt(x - 3)

Step-by-step explanation:

Hope you won't mind the correction, but that's y = x^2 + 3. Use " ^ " to indicate exponentiation.

Starting with y = x^2 + 3, interchange x and y:

x = y^2 + 3

Next, solve for y: y^2 = x - 3, or y = +sqrt(x - 3).

Note that we'd normally write "plus or minus sqrt(x - 3)," but that would provide two y values for each x value (which violates the definition of "function').

Finally, replace "y" with the inverse function label:

-1

f (x) = sqrt(x - 3)

Step2247 [10]3 years ago

3 0

y = the square root of (x-3)

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sasho [114]

$\displaystyle 5^{1+\log_4 x}+5^{-\log_4x-1} = \frac{26}{5}\\ \\
\text{Sea } z=5^{1+\log_4 x} \text{ entonces}: \\ \\
z+\frac{1}{z}=\frac{26}{5}\\ \\
5z^2-26z+5=0 \\ \\
(5z-1)(z-5)=0 \\ \\
z\in\left\{\frac{1}{5};5\right\}\\ \\
\text{Then: }\\ \\
5^{1+\log_4x}=5^{-1} \vee 5^{1+\log_4x}=5\\ \\
1+\log_4x=-1 \vee 1+\log_4x=1\\ \\
\log_4x =-2 \vee \log_4x=0 \\ \\
x=\frac{1}{16} \vee x=1\\ \\
\text{Answer: }x\in\left\{\frac{1}{16};1\right\}
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