Equations that look different but have the same solution are said to be

1 answer:

3 0

Let's define each choice to differentiate which is the answer

A. Equivalent - equivalent equations may not look exactly the same on face value. But they are equivalent because they have the same exact solution.

B. Expressions - expression is a general term for equations that are formed from word problems

C. Equal - equal equations are the exact duplicate of each other

D. Similar - this term is only used on geometric shapes to tell that the two shapes have a fixed ratio of their similar sides or angles

E. Radical - radical equations are those involving fractions

Therefore, from their descriptions, the answer is A.

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If a(x) = 3x + 1 and b(x)= squareroot x-4, what is the domain of (b*a)(x)?

oksano4ka [1.4K]

$\boxed{ \ x \geq 1 \ }$ or can be written as $\boxed{ \ [1, \infty) \ }$

<h3>Further explanation</h3>

This is a question about the composition of functions and how to get a domain function.

Given $\boxed{ \ a(x) = 3x + 1 \ }$ and $\boxed{ \ b(x) = \sqrt{x - 4} \ }$ .

We will form (b o a)(x) and then determine the domain.

$\boxed{ \ (b \circ a)(x) = b(a(x)) \ }$

Replace each appearance of x in b(x) with $\boxed{ \ a(x) = 3x + 1 \ }$ .

$\boxed{ \ (b \circ a)(x) = \sqrt{(3x + 1) - 4} \ }$

Thus, $\boxed{ \ (b \circ a)(x) = \sqrt{3x - 3} \ }$

To be defined, the value under the radical sign must not be negative. Therefore, the domain of $(b \circ a)(x) = \sqrt{3x - 3}$ are processed as follows.

$\boxed{ \ 3x - 3 \geq 0 \ }$

Both sides added by 3.

$\boxed{ \ 3x \geq 3 \ }$

Both sides divided by 3.

$\boxed{ \ x\geq 1 \ }$

Thus, the domain of $(b \circ a)(x) = \sqrt{3x - 3}$ is $\boxed{ \ x \geq 1 \ }$ or can be written as $\boxed{ \ [1, \infty) \ }$

<h3>Learn more</h3>

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Keywords: composition of function, if a(x) = 3x + 1, and, b(x) = √(x-4), what is the domain of, (b o a)(x), b(a(x)), defined, the value, under the radical sign, must not be negative,