Solve. Check for extraneous solutions

This equation has no solutions on the real-valued logarithm.

Step-by-step explanation:

Raise both sides to the 8th power:

11-6x = 1-x

10 = 5x

x = 2

Plug this in:

log(11 - 6(2)) = log(11 -12) = log(-1); this is NOT a valid solution on a real-valued logarithm.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2