Which equation is the inverse of 5 y + 4 = (x + 3) squared + one-half?

Mathematics

2 answers:

telo118 [61]3 years ago

8 0

Answer:

The correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot

Step-by-step explanation:

the given equation is $5y + 4 =(x+3)^{2} + \frac{1}{2}$

Therefore we can write $5y\hspace{0.1cm} = (x+3)^{2} + \frac{1}{2} - 4 \hspace{0.3cm} \Rightarrow \hspace{0.2cm} 5y = (x+3)^{2} - \frac{7}{2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} y = \frac{(x+3)^{2}}{5} - \frac{7}{10}$

To find the inverse of the above function let us replace x with y and y with x.

Therefore we get

$x = \frac{(y+3)^{2}}{5} - \frac{7}{10}$

Now we write the above equation with only y on the Left hand side and we will obtain the inverse of the given function

$y = \pm \sqrt{5 (x + \frac{7}{10} )} \hspace{0.1cm} - \hspace{0.1cm} 3 \hspace{0.1cm} \Rightarrow\hspace{0.1cm} y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}$

Therefore the correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot , $y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}$