Question

find domain and range of the function 7x^2+4x-1​

Answer 1

Answer:

this is your solution for the following information

Answer 2

Domain is set of all real numbers,

Range is all real numbers greater than equal to -11/7

Step-by-step explanation:

Given function,

$7x^2 + 4x - 1$

Which is a quadratic.

Since, the quadratic function is defined for all real numbers,

Thus, Domain = set of all real numbers,

Now,

$7x^2 + 4x - 1$

$7(x^2 +\frac{4}{7}x ) - 1$

$7(x^2 +\frac{4}{7}x ) - 1$

$7(x+\frac{2}{7})^2 -1 - \frac{4}{7}$

$7(x+\frac{2}{7})^2-\frac{11}{7}$

We know that,

the vertex of a quadratic function $a(x-h)^2+k$ is (h, k)

By comparing,

Vertex of the given function = (-2/7, -11/7 )

Since, the quadratic function with positive leading coefficient gives minimum value at its vertex.

Thus, Range = all real numbers greater than equal to -11/7

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