The given functions were
\(h(x)=2x+5\: and\:g(x)=8-3x\)
Before we can evaluate \(h(g(1.5))\) we need to find an expression for \(h(g(x))\).
This is the composition of the two functions. \(h(g(x))\) means \(g(x)\) becomes an input for \(h(x)\). This means that;
\(h(g(x))=h(8-3x)\)
So we need to substitute, \(8-3x\) wherever we see \(x\) in \(h(x)\)
\(\Rightarrow h(g(x))=2(8-3x)+5\)
We expand the bracket to obtain;
\(h(g(x))=2\times8-2\times3x+5\)
Simplify to obtain;
\(h(g(x))=16-6x+5\)
\(h(g(x))=21-6x\)
Now we substittute \(x=1.5\) in to \(h(g(x))=21-6x\) to obtain,
\(\Rightarrow h(g(1.5))=21-6(1.5)\)
\(\Rightarrow h(g(1.5))=21-9\)
\(\Rightarrow h(g(1.5))=12\)
Hence, the value of \(h(g(1.5))\) is \(1.5\).
