4 years ago

Evaluate this expression: (1/5 x 5) ^5

Mathematics

1 answer:

Reika [66]4 years ago

5 0

Answer:

The answer is x ^5

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Write each expression in a simpler form that is equivalent to the given expression. Let F be a nonzero number. f-4

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given f(x)=3^x-2 and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur b

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Answer:

$g(x)=3^{3x}+2$

The transformation that occurs from $f(x)\rightarrow g(x)$ is compression by 3 units horizontally and shift of 4 units upwards.

Step-by-step explanation:

Given

$f(x)=3^x-2$

$g(x)=f(3x)+4$

Translation Rules:

$f(x)\rightarrow f(cx)$

If $c>1$ the function is compressed $c$ units horizontally.

If $c$ and $c>0$ the function stretches $c$ units horizontally.

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying the rules to $f(x)$

Step 1

$f(x)\rightarrow f(3x)$

$f(3x)=3^{3x}-2$

[compressed $3$ units horizontally]

Step 2

$f(3x)\rightarrow f(3x)+4=g(x)$

$f(3x)+4=3^{3x}-2+4$

∴ $g(x)=3^{3x}+2$

[shifts 4 nits up]

∴ The transformation that occurs from $f(x)\rightarrow g(x)$ is compression by 3 units horizontally and shift of 4 units upwards.

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Substitute x for 3 & y for -2

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