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Nataliya [291]
4 years ago
9

Find the linear transformation model of log y^=0.6021

Mathematics
1 answer:
11111nata11111 [884]4 years ago
7 0
In its current format, the equation is in a logarithmic equation.  
To convert to a linear equation the log transformation must be removed.
 To remove the log transformation, one must multiply both sides of the
equation by the "opposite" or "reverse" of the log function. 
 Since it is not otherwise indicated, it can be assumes this is a base 10 log. 
 To reverse a base 10 log the function is converted to 10^x, where x is the function.
 Therefore:
 log y=0.6021
 10^(log y)=10^(0.6021)
 y=10^(0.6021)
 y=4
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n200080 [17]

Given:

f(x)=\dfrac{8}{x}

g(x)=\dfrac{8}{x}

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

f(g(x))=x and g(f(x))

We have,

f(x)=\dfrac{8}{x}

g(x)=\dfrac{8}{x}

Now,

f(g(x))=f(\dfrac{8}{x})              [\because g(x)=\dfrac{8}{x}]

f(g(x))=\dfrac{8}{\dfrac{8}{x}}            [\because f(x)=\dfrac{8}{x}]

f(g(x))=8\times \dfrac{x}{8}

f(g(x))=x

Similarly,

g(f(x))=f(\dfrac{8}{x})              [\because f(x)=\dfrac{8}{x}]

g(f(x))=\dfrac{8}{\dfrac{8}{x}}            [\because g(x)=\dfrac{8}{x}]

g(f(x))=8\times \dfrac{x}{8}

g(f(x))=x

Since, f(g(x))=x and g(f(x)), therefore, f(x) and g(x) are inverse of each other.

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