Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 64

$a=5, -5$

We have: $f(x)=3x^2 -7$ and $g(x)=2x+a$ $(f \circ g)$ crosses the y-axis at 68. This implies that $(f \circ g)(0)=68$ Now, $g(0)=(2)(0)+a =a$ So, $(f\circ g) (0) =f[g(0)]=f(a)=3a^2-7=683$ The above equation can be simplified as: $3a^2=75 \\ a^2=25 \\ a=\pm 5=5, -5$